Answer:
[tex]cos(-\theta) = -0.73[/tex]
Step-by-step explanation:
It is given that:
[tex]sin(\theta -\dfrac{\pi}{2}) = 0.73[/tex]
Formula to be used:
[tex]1.\ sin(-x) = -sinx\\2.\ sin(\dfrac{\pi}{2}-x) = cosx\\3.\ cos(-x) = cosx[/tex]
Using Formula (1) written above:
[tex]\Rightarrow sin (\theta - \dfrac{\pi}{2})=sin(-(\dfrac{\pi}{2}-\theta ))\\\Rightarrow -sin(\dfrac{\pi}{2}-\theta)[/tex]
Now, using Formula (2) written above:
[tex]\Rightarrow -sin(\dfrac{\pi}{2}-\theta) = -cos \theta[/tex]
So, we can say that:
[tex]sin(\theta -\dfrac{\pi}{2}) = -cos\theta = 0.73 ...... (1)[/tex]
We have to find the value of [tex]cos(-\theta)[/tex].
Using Formula (3) written above:
[tex]cos(-\theta) = cos\theta[/tex]
So, ultimately we need to find the value of [tex]cos\theta[/tex]
Using equation (1):
[tex]-cos\theta = 0.73\\\Rightarrow cos\theta = -0.73[/tex]
So, the answer is [tex]cos(-\theta) = -0.73[/tex].
What is the solution to this equation?
10x - 3(x- 6) = x + 30
O A. x = 8
O B. x = 2
C. X= 4
[tex]answer \\ 2\\ solution \\ 10x - 3(x - 6) = x + 30 \\ or \: 10x - 3x + 18 = x + 30 \\ or \: 10x - 3x - x = 30 - 18 \\ or \: 7x - x = 12 \\ or \: 6x = 12 \\ or \: x = \frac{12}{6} \\ x = 2 \\ hope \: it \: helps[/tex]
Answer:
x=2
Step-by-step explanation:
10x - 3(x- 6) = x + 30
Distribute
10x -3x+18 = x+30
Combine like terms
7x + 18 = x+30
Subtract x from each side
6x+18 = 30
Subtract 18 from each side
6x = 30-18
6x = 12
Divide by 6
6x/6 = 12/6
x =2
Which of the following is a geometric sequence?
Answer:
D. 1, 1/2, 1/4, 1/8, ...
Step-by-step explanation:
Only one of the listed is a geometric sequence:
D. 1, 1/2, 1/4, 1/8, ... with the common ratio 1/2Suppose U.S. consumers 21 years and older consumed 26.4 gallons of beer and cider per person during 2017. A distributor in Milwaukee believes that beer and cider consumption are higher in that city. A sample of consumers 21 years and older in Milwaukee will be taken, and the sample mean 2017 beer and cider consumption will be used to test the following null and alternative hypotheses:
H0: μ ≤ 26.4
Ha: μ > 26.4
(a) Assume the sample data led to rejection of the null hypothesis. What would be your conclusion about consumption of beer and cider in Milwaukee?
a) Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons and hence lower than throughout the United States.
b) Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons and hence higher than throughout the United States.
c) Conclude that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons and hence higher than throughout the United States.
d) Conclude that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons and hence lower than throughout the United States.
(b) What is the Type I error in this situation? What are the consequences of making this error?
a) The type I error is rejecting H0 when it is true. This error would claim the consumption in Milwaukee is greater than 26.4 when it is actually less than or equal to 26.4.
b) The type I error is not rejecting H0 when it is true. This error would claim the consumption in Milwaukee is less than or equal to 26.4 when it is actually less than or equal to 26.4.
c) The type I error is not rejecting H0 when it is false. This error would claim the consumption in Milwaukee is less than or equal to 26.4 when it is actually greater than 26.4.
d) The type I error is rejecting H0 when it is false. This error would claim the consumption in Milwaukee is greater than 26.4 when it is actually greater than 26.4.
(c) What is the Type II error in this situation? What are the consequences of making this error?
a) The type II error is accepting H0 when it is true. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons when it is less than or equal to 26.4.
b) The type II error is not accepting H0 when it is true. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons when it is not.
c) The type II error is accepting H0 when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons when it is not.
d) The type II error is not accepting H0 when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons when it is greater than 26.4.
Answer:
Step-by-step explanation:
A. If the null hypothesis was rejected, the conclusion would be
b) Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons and hence higher than throughout the United States.
B. The correct option is
a) The type I error is rejecting H0 when it is true. This error would claim the consumption in Milwaukee is greater than 26.4 when it is actually less than or equal to 26.4.
C. The correct option is
c) The type II error is accepting H0 when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons when it is not.
A 50 ft kite string is flying on the beach above an umbrella. You are holding the end
of the string and are 12 feet from the umbrella. How high in the air is the kite flying?
Round to the nearest degree.
Answer:
The height of the kite is 48.54 feet
The angle of elevation is 76.11°
Step-by-step explanation:
To find the height of the kite, we can use the Pythagoras' theorem in the triangle created by the length of the string (hypotenuse), the height of the kite and the distance to the umbrella (catheti).
Then, we have:
50^2 = 12^2 + height^2
height^2 = 2500 - 144
height^2 = 2356
height = 48.54 ft
So the kite is 48.54 feet high in the air.
The angle of elevation can be calculated using the cosine relation:
cos(angle) = 12 / 50
cos(angle) = 0.24
angle = 76.11°
What translation was used to ABCD to produce A’ B’C’D’
What percentage of the total number of microstates are in one of the three most likely macro states of 100 coins being tossed (49 heads and 51 tails, 50 heads and 50 tails, or 51 heads and 49 tails)
Answer:
Step-by-step explanation:
Idk
Which of the following sets would have a graph with an open circle on 5 and a ray pointing right on the number line?
The open circle means we do not include the endpoint, hence the use of a greater than symbol. If we were to include the endpoint, then we'd have greater than or equal to. We can rule out choice B due to this reasoning.
The ray pointing to the right indicates we are talking about x values larger than 5, so we can rule out choice A and conclude the answer is C.
Side note: The notation [tex]x \in \mathbb{R}[/tex] is saying "x is a real number"
(like Ross 6.28) The time that it takes to service a car is an exponential random variable with rate 1. (a) If Lightning McQueen (L.M.) brings his car in at time 0 and Sally Carrera (S.C) brings her car in at time t, what is the probability that S.C.’s car is ready before L.M.’s car? Assume that service times are independent and service begins upon arrival of the car.
Answer: provided in the explanation section
Step-by-step explanation:
The complete question says:
The time that it takes to service a car is an exponential random variable with rate 1. (a) If Lightning McQueen (L.M.) brings his car in at time 0 and Sally Carrera (S.C) brings her car in at time t, what is the probability that S.C.'s car is ready before L.M.'s car? Assume that service times are independent and service begins upon arrival of the car Be sure to: 1) define all random variables used, 2) explain how independence of service times plays a part in your solution, 3) show all integration steps. (b) If both cars are brought in at time 0, with work starting on S.C. 's car only when L.M.'s car has been completely serviced, what is the probability that S.C.'s car is ready before time 2?
Ans to this is provided in the images uploaded as it is not possible to put the symbols here...
i hope you find this helpful.
cheers !!
An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a random variable with variance = 5.
a) What is the probability that at most 3 cars per year will experience a catastrophe?
b) What is the probability that more than 1 car per year will experience a catastrophe?
Answer:
(a) Probability that at most 3 cars per year will experience a catastrophe is 0.2650.
(b) Probability that more than 1 car per year will experience a catastrophe is 0.9596.
Step-by-step explanation:
We are given that the distribution of the number of cars per year that will experience the catastrophe is a Poisson random variable with variance = 5.
Let X = the number of cars per year that will experience the catastrophe
SO, X ~ Poisson([tex]\lambda = 5[/tex])
The probability distribution for Poisson random variable is given by;
[tex]P(X=x) = \frac{e^{-\lambda} \times \lambda^{x} }{x!} ; \text{ where} \text{ x} = 0,1,2,3,...[/tex]
where, [tex]\lambda[/tex] = Poisson parameter = 5 {because variance of Poisson distribution is [tex]\lambda[/tex] only}
(a) Probability that at most 3 cars per year will experience a catastrophe is given by = P(X [tex]\leq[/tex] 3)
P(X [tex]\leq[/tex] 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= [tex]\frac{e^{-5} \times 5^{0} }{0!} +\frac{e^{-5} \times 5^{1} }{1!} +\frac{e^{-5} \times 5^{2} }{2!} +\frac{e^{-5} \times 5^{3} }{3!}[/tex]
= [tex]e^{-5} +(e^{-5} \times 5) +\frac{e^{-5} \times 25 }{2} +\frac{e^{-5} \times 125}{6}[/tex]
= 0.2650
(b) Probability that more than 1 car per year will experience a catastrophe is given by = P(X > 1)
P(X > 1) = 1 - P(X [tex]\leq[/tex] 1)
= 1 - P(X = 0) - P(X = 1)
= [tex]1-\frac{e^{-5} \times 5^{0} }{0!} -\frac{e^{-5} \times 5^{1} }{1!}[/tex]
= 1 - 0.00674 - 0.03369
= 0.9596
What is the mode of this set of data?
Answer:
The mode is 15
Step-by-step explanation:
The mode is the number which appears most often in a set of numbers. Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6 (it occurs most often).
Answer:
The mode of this set is 15.
Step-by-step explanation:
the mode is 15 bcoz 15 is repeated two times where as other numbers aren't repeated..
A car is discounted 10% and sells for $15,673. What was the discount amount?
Answer:
$1741.44
Step-by-step explanation:
The discounted amount is 100% -10% = 90% of the original. The amount of the discount is 10% of the original, or 1/9 of the discounted amount:
10% = 90% × 1/9
The discount was ...
$15,673/9 = 1,741.44
_____
Check
The original is the sum of the discounted amount and the discount:
original price = $15,673.00 +1,741.44 = $17, 414.44
10% of that value is 1,741.44, as shown above.
According to the Rational Root Theorem, Negative two-fifths is a potential rational root of which function?
f(x) = 4x4 – 7x2 + x + 25
f(x) = 9x4 – 7x2 + x + 10
f(x) = 10x4 – 7x2 + x + 9
f(x) = 25x4 – 7x2 + x + 4
Answer:
Neither expression satisfies the given rational root.Step-by-step explanation:
To find the right answer, we just need to replace the given root in each expression and see which one gives zero.
First expression.[tex]f(x)=4x^{4} -7x^{2} +x+25\\f(-\frac{2}{5})= 4(-\frac{2}{5})^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+25=\frac{64}{625}-\frac{28}{25} -\frac{2}{5} +25 \approx 23.58[/tex]
Second expression.[tex]f(x)=9x^{4}-7x^{2} +x+10=9(-\frac{2}{5} )^{4} -7(-\frac{2}{5} )^{2} +\frac{2}{5} +10 \approx 9.5[/tex]
Third expression.[tex]f(x)=10x^{4}-7x^{2} +x+9=10(-\frac{2}{5} )^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+9 \approx 7.7[/tex]
Fourth expression.[tex]f(x)=25x^{4}-7x^{2} +x+4=25(-\frac{2}{5} )^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+4 \approx 3.12[/tex]
Therefore, neither expression satisfies the given rational root.
Answer:
D. f(x) = 25x^4 - 7x^2 + x + 4.
Step-by-step explanation:
The correct answer to your question is D.
For 120 consecutive days, a process engineer has measured the temperature of champagne bottles as they are made ready for serving. Each day, she took a sample of 8 bottles. The average across all 960 bottles (120 days, 8 bottles per day) was 46 degrees Fahrenheit. The standard deviation across all bottles was 0.8 degree.Round your answer to 4 digits after the decimal point if it is not an integer. Do NOT use comma in your numeric answers.Sample size is .Number of samples is .When constructing a x-bar chart:The center line should be .ESD(x-bar) equals .The upper control limit (UCL) should be .The lower control limit (LCL) should be .
Answer:
Center line = 46
UCL = 46.84852
LCL = 45.15148
Step-by-step explanation:
Given:
Standard deviation = 0.8
Mean, u = 46
Sample size, n= 8
First calculate the estimated standard deviation:
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{0.8}{\sqrt{8}} = 0.282843[/tex]
a) The center line, X', would be the average across all components. Here the average across all 960 bottles is 46
Therefore,
[tex] X' = 46 [/tex]
b) The upper control limit, UCL:
UCL = u + 3s
= 46 + 3(0.28284)
= 46 + 0.84852
= 46.84852
c) The upper control limit, LCL:
LCL = u + 3s
= 46 - 3(0.28284)
= 46 - 0.84853
= 45.15148
What is the length of AC
Answer:
5.8
Step-by-step explanation:
The angle bisector makes the triangle sides on either side of it proportional.
AC/CD = AB/BD
AC = CD·AB/BD
AC = 2(8.1/2.8) = 8.1/1.4 ≈ 5.7857 . . . . substitute shown values, evaluate
AC ≈ 5.8
The table represents a function. A 2-column table with 5 rows. The first column is labeled x with entries negative 6, 7, 4, 3, negative 5. The second column is labeled f of x with entries 8, 3, negative 5, negative 2, 12. Which value is an output of the function? –6 –2 4 7The table represents a function. A 2-column table with 5 rows. The first column is labeled x with entries negative 6, 7, 4, 3, negative 5. The second column is labeled f of x with entries 8, 3, negative 5, negative 2, 12. Which value is an output of the function? –6 –2 4 7
Answer:
-2 is an output of the function.
Step-by-step explanation:
The given table is as follows:
[tex]\left[\begin{array}{cc}{x}&f(x)\\-6&8\\7&3\\4&-5\\3&-2\\-5&12\end{array}\right][/tex]
Here, the values written on the left side of table i.e. values of [tex]x[/tex] are known as the domain values or input values to a function.
The values written on the right side of table i.e. values of [tex]f(x)[/tex] are known as the range values or output values of the function [tex]f(x)[/tex].
Let us consider the pairs of values:
(-6,8) then left side value is of [tex]x[/tex] and right side value is of [tex]f(x)[/tex]
i.e. when [tex]x=-6[/tex], the output value [tex]f(x) =8[/tex].
The same thing applies for all the pairs of values.
similarly for the pair (3,-2):
Left side value is of [tex]x[/tex] and right side value is of [tex]f(x)[/tex]
i.e. when [tex]x=3[/tex], the output value [tex]f(x) =-2[/tex].
So, the answer is:
-2 is an output of the function.
Answer:
-2
Step-by-step explanation:
A fuel oil tank is an upright cylinder, buried so that its circular top is 8 feet beneath ground level. The tank has a radius of 6 feet and is 18 feet high, although the current oil level is only 12 feet deep. Calculate the work required to pump all of the oil to the surface. Oil weighs 50\, \hbox{lb/ft}^3.
Answer:
1.504×10⁶ ft·lb
Step-by-step explanation:
We understand the top of the oil in the tank is 12 ft below ground level, and the bottom of the tank is 8+18=26 ft below ground level. Then the average depth of the oil is (12+26)/2 = 19 ft below ground level.
The height of the oil in the tank is 26-12=14 ft, so the volume of it is ...
V = πr²h = π(6 ft)²(14 ft) = 504π ft³ ≈ 1583.36 ft³
__
So, the work required to raise that volume of oil to the surface is ...
(1538.36 ft³)(50 lb/ft³)(19 ft) = 1.504×10⁶ ft·lb
Please answer this correctly
Answer:
Bailey: 16%
Coco: 28%
Ginger: 32%
Ruby: 24%
I hope this helps!
(-1/4 - 1/2) ÷ (-4/7)
Answer:
1 5/16
Step-by-step explanation:
(-1/4 - 1/2) ÷ (-4/7)
PEMDAS says parentheses first
Get a common denominator
(-1/4 - 2/4) ÷ (-4/7)
(-3/4) ÷ (-4/7)
Copy dot flip
-3/4 * -7/4
21/16
Change to a mixed number, 16 goes into 21 1 time with 5 left over
1 5/16
2/5 of the members of a school band are 6th graders. What percent of
the students in the band are non-sixth graders?
Answer:
60%
Step-by-step explanation:
3/5 is 60%
Answer:
60%
Step-by-step explanation:
5/5 minus 2/5 is 3/5
5 divided by 3 is .6
in order to find out the percent move the decimal over to the right
I really need help :( anybody ??
_______________________________
Hey!!
Answer:{2,4,5}
Explanation:
RangeLet R be relation from A to B.The set of second components or the set of elements of B are called range.
Hope it helps..
_______________________________
A researcher reports that the farther college students are from their parents, the more often they communicate with their parents (either by phone or by e-mail). Is this an example of a positive correlation or a negative correlation?
Answer:
Positive correlation
Step-by-step explanation:
A positive correlation exists between two variables, when both variables tend to move along the same direction. In order words, when one particular variable increases, there is also an increase in the other variable.
The case stated above is an example of positive correlation, because, the farther the students are from their parents, the more often they communicate with them. As distance increases, so does the number of, perhaps, phone calls increases as well.
Answer:
Positive correlation
Step-by-step explanation:
A positive correlation occurs whereby in a relationship between two variables, both variable move in the same direction meaning as one increases, the other also increases.
In this study, an increase in distance enforces an increase in communication with the parents.
Find the area of the following square.
Write your answer in simplest form.
Be sure to include the correct unit in your answer.
4 1/2m
Answer:
[tex]20.25 \: m^2[/tex]
Step-by-step explanation:
Use the formula for the area of a square.
[tex]A=s^2[/tex]
Where [tex]s=4.5[/tex]
[tex]s^2\\(4.5)^2\\20.25[/tex]
The area of the square is 20.25 square meters as per the concept of the square.
To find the area of a square, we need to square the length of one of its sides. In this case, the side length is given as 4 1/2 meters.
First, we need to convert the mixed number 4 1/2 into an improper fraction. We can rewrite it as 9/2.
Next, we square the side length:
[tex]\frac{9}{2}^2 = \frac{81}{4}[/tex].
To simplify the fraction, we can divide the numerator by the denominator:
81 ÷ 4 = 20 remainders 1.
Therefore, the area of the square is 20 1/4 square meters.
However, we can simplify the mixed number further. Since 4 can be divided by 4 and 1 can be divided by 4, we have:
20 1/4
= 20 + 1/4
= 20 + 1/4
= 20 + 0.25
= 20.25.
Therefore, the area of the square is 20.25 square meters.
To learn more about the square;
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If the ratio of the ages of Kissi and Esinam is 3:5 and that of Esinam and Lariba is 3:5 and
the sum of the ages of all 3 is 147 years, what is the age difference between oldest the
youngest
Answer:
The age difference between the youngest and the oldest is 48
How do I find the value of x for which line a is parallel to line b?
Answer:
x = 20
Step-by-step explanation:
3x + 6x = 180, if you make them supplementary then they will be parallel
9x = 180
x = 20
Will mark brainliest! Thanks ! and like if you can please explain it cuz I want to understand it to :)
Answer: F.) 7 triangles
Step-by-step explanation:
Congruent means completely equal in side lengths and angles. Think of this weird figure like 4 triangles that are see through and are covering a diamond underneath
Of those 4 "see through triangles", there are 3 equal to ΔABC
Now on the diamond underneath, there is another 4. Its hard to actually explain what I mean, but take two triangles from that dimaond. Theyre gonna be congruent to ΔABC.
That's 4 + 3 = 7 total triangles
What is the measure of
55°
The sum or measures of interior angle in a triangle is 180°.
Angle A, 35° + Angle C, 90° =125°
Angle B= 180°-125°=55°[angle B]
Estimate the quotient 241 ÷ 5. A. 40 B. 250 C. 50 D. 60
Answer:
The quotient of 241 ÷ 5 is 48.
Step-by-step explanation:
Division is splitting into equal parts or groups.
The quotient is the answer after we divide one number by another.
To find the quotient 241 ÷ 5 you must:
Write the problem in long division format
[tex]5\overline{|\smallspace241}[/tex]
Divide 24 by 5 to get 4
Multiply the quotient digit 4 by the divisor 5
Subtract 20 from 24
Bring down the next number of the dividend
Divide 41 by 5 to get 8
Multiply the quotient digit 8 by the divisor 5
Subtract 40 from 41
[tex]\mathrm{The\:solution\:for\:Long\:Division\:of}\:\frac{241}{5}\:\mathrm{is}\:48\:\mathrm{with\:remainder\:of}\:1\\\\48\quad \mathrm{Remainder}\quad \:1[/tex]
16. Model with Math What must be the sum of
the two remaining numbers, x and y? Write an
equation to show how to find this sum.
Answer:
The sum of the two remaining numbers, x and y = 60
Question:
The question isn't clear enough as some information have been omitted. Let's consider the following:
Model with Math. The average of six numbers is 18. If the average of four numbers is 12. What must be the sum of the two remaining numbers, x and y?
Write an equation to show how to find this sum.
Step-by-step explanation:
Mathematical models are applied to represent things in the real world in order to solve problems.
The formula we would use to solve this problem is an example of a mathematical model.
Types of mathematical model we can use include equations and graphs.
Using equations:
Average of six numbers = 18
Average of four of the numbers = 12
Total sum of the four numbers = 4×12 = 48
the two unknown numbers are x and y
Average of six numbers = (Sum of all 6 numbers)/6
=(Total sum of four numbers + x + y)/6
(48 + x + y)/6 = 18
The equation that shows how to find the sum:
(1/6)(48 + x + y) = 18
48 + x + y = 18×6
48 + x + y = 108
x + y = 108-48
x+y = 60
The sum of the two remaining numbers, x and y = 60
A clothing store determines that in order to sell x shirts, the price per shirt should be p(x)=100−x dollars. Getting x shirts from the supplier costs the store C(x)=1,600+20x dollars. If the store’s revenue from selling x shirts is R(x)=x⋅p(x), for what value of x will the store’s cost and revenue be equal?
Answer:
x= -40
Step-by-step explanation:
Cost
C(x)=1,600+20x
P(x)=100-x
Revenue=x*p(x)
=x*(100-x)
=100x-x^2
Cost=Revenue
1600+20x=100x-x^2
1600+20x-100x+x^2=0
1600-80x+x^2=0
Solve using quadratic formula
Formula where
a = 1, b = 80, and c = 1600
x=−b±√b2−4ac/2a
x=−80±√80^2−4(1)(1600) / 2(1)
x=−80±√6400−6400 / 2
x=−80±√0 / 2
The discriminant b^2−4ac=0
so, there is one real root.
x= −80/2
x= -40
Suppose that the functions p and q are defined as follows.
Answer:
Step-by-step explanation:
Hello,
qop(2)=q(p(2))
p(2) = 4+3=7
[tex]q(7) = \sqrt{7+2}=\sqrt{9}=3[/tex]
so
qop(2)=3
and poq(2)=p(q(2))
[tex]q(2)=\sqrt{2+2} = \sqrt{4}=2[/tex]
p(2) = 7
so poq(2)=7
thanks
The answer is "[tex]\bold{(q \circ p)(2)= 3}\ and \ \bold{(p \circ q)(2)=7}[/tex]" and the further explanation can be defined as follows;
Given:
[tex]\to \bold{p(x)=x^2+3}\\\\\to \bold{q(x)=\sqrt{x+2}}[/tex]
Find:
[tex]\bold{(q \circ p)(2)=?}\\\\\bold{(p \circ q)(2)=?}[/tex]
Solve the value for [tex]\bold{(q \circ p)(2)}\\\\[/tex]:
[tex]\to \bold{(q \circ p)(2)= q \circ p(2) =q(p(2))}\\\\[/tex]
[tex]\therefore\\\\ \to \bold{p(2)=2^2+3= 4+3=7}\\\\\ \because \\\\ \to \bold{q(p(2))=\sqrt{7+2}=\sqrt{9}=3}[/tex]
Solve the value for [tex]\bold{(p \circ q)(2)}\\\\[/tex]:
[tex]\to \bold{(p \circ q)(2)= p \circ q(2)= p (q(2))}\\\\[/tex]
[tex]\therefore\\\\ \to \bold{q(2)=\sqrt{2+2}=\sqrt{4}=2}\\\\\ \because \\\\ \to \bold{p(q(2))=2^2+3= 4+3=7}[/tex]
Therefore the final answer of "[tex]\bold{(q \circ p)(2)= 3}\ and \ \bold{(p \circ q)(2)=7}[/tex]"
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